How can an OBJ sequence be converted to an FBX animation?
If you can guarantee the same number of vertices will appear in the same order in each .obj file (such as a single character model exported to individual frames), you could accomplish this by interpreting the vertex movements mesh transformations on import. Otherwise, you're stuck with entirely separate objects on each frame.

I don't know of any off-the-shelf versions of this, though the stop-motion script you mention in your question could be modified to work this way (in particular, the bakeSequence() function which creates a separate mesh object per-frame).